منابع مشابه
Directed domination in oriented hypergraphs
ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...
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The celebrated Erdős-Ko-Rado theorem shows that for n > 2k the largest intersecting k-uniform set family on [n] has size ( n−1 k−1 ) . It is natural to ask how far from intersecting larger set families must be. Katona, Katona and Katona introduced the notion of most probably intersecting families, which maximise the probability of random subfamilies being intersecting. We consider the most prob...
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A hypergraph is 2-intersecting if any two edges intersect in at least two vertices. Blais, Weinstein and Yoshida asked (as a first step to a more general problem) whether every 2-intersecting hypergraph has a vertex coloring with a constant number of colors so that each hyperedge has at least min{|e|, 3} colors. We show that there is such a coloring with at most 5 colors (which is best possible...
متن کاملOn intersecting hypergraphs
We investigate the following question: “Given an intersecting multi-hypergraph on n points, what fraction of edges must be covered by any of the best 2 points?” (Here “best” means that together they cover the most.) We call this M2(n). This is a special case of a question asked by Erdős and Gyárfás [1] (they considered r–wise intersecting and the best t points), and is a generalization of work ...
متن کاملCross-intersecting pairs of hypergraphs
Two hypergraphs H1, H2 are called cross-intersecting if e1 ∩ e2 ̸= ∅ for every pair of edges e1 ∈ H1, e2 ∈ H2. Each of the hypergraphs is then said to block the other. Given integers n, r,m we determine the maximal size of a sub-hypergraph of [n]r (meaning that it is r-partite, with all sides of size n) for which there exists a blocking sub-hypergraph of [n]r of size m. The answer involves a sel...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2018
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.05.039